Unsupervised depth prediction neural networks

ABSTRACT

A system for generating a depth output for an image is described. The system receives input images that depict the same scene, each input image including one or more potential objects. The system generates, for each input image, a respective background image and processes the background images to generate a camera motion output that characterizes the motion of the camera between the input images. For each potential object, the system generates a respective object motion output for the potential object based on the input images and the camera motion output. The system processes a particular input image of the input images using a depth prediction neural network (NN) to generate a depth output for the particular input image, and updates the current values of parameters of the depth prediction NN based on the particular depth output, the camera motion output, and the object motion outputs for the potential objects.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application Ser.No. 62/727,502, filed on Sep. 5, 2018. The disclosure of the priorapplication is considered part of and is incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to processing images using neural networks.

Machine learning models receive an input and generate an output, e.g., apredicted output, based on the received input. Some machine learningmodels are parametric models and generate the output based on thereceived input and on values of the parameters of the model.

Some machine learning models are deep models that employ multiple layersof models to generate an output for a received input. For example, adeep neural network is a deep machine learning model that includes anoutput layer and one or more hidden layers that each apply a non-lineartransformation to a received input to generate an output.

SUMMARY

This specification describes a neural network system implemented ascomputer programs on one or more computers in one or more locations thatincludes a camera motion estimation neural network, an object motionestimation neural network, and a depth prediction neural network.

Particular embodiments of the subject matter described in thisspecification can be implemented so as to realize one or more of thefollowing advantages. The subject matter described in this specificationis generally directed to unsupervised learning techniques that allow aneural network system to predict depth and ego-motion directly frommonocular videos more accurately and more efficiently than conventionalapproaches. While precise depth prediction for moving objects andprecise ego-motion estimation are crucial for many odometry-based tasks,i.e., tasks that require the use of data from, motion sensors toestimate change in position over time (e.g., robot navigation in dynamicscenes), prior work mainly focuses on camera ego-motion, leaving objectmotions unaddressed. In contrast, the described techniques explicitlymodel individual objects' motion in 3D together with camera ego-motion,thereby producing more precise depth and ego-motion estimation results.

In addition, prior work that employs supervised learning methodsrequires expensive depth sensors, which may not be readily available inmost robotics scenarios and may introduce their own sensor noise. Incontrast, the subject matter described herein addresses unsupervisedlearning of scene depth, camera motions and objection motions wheresupervision is provided by monocular videos taken by a camera—the leastexpensive, least restrictive, and most ubiquitous sensor for robotics.No additional supervision or sensors are necessary. This ensures thattraining data for the training of depth, object motion and camera motionneural networks is readily available, i.e., because large quantities ofunlabeled monocular videos can be easily gathered during the course ofnormal operation of a robotic agent. Thus, the techniques describedherein are applicable in most robotics scenarios.

Furthermore, the techniques described herein explicitly model 3D motionsof individual moving objects in the scene as depicted in input images,together with camera ego-motion. By introducing the local structure ofthe input images into the learning process, the techniques enable theneural network system to adapt to new environments by learning with anonline refinement (also referred to as “online fusion”) of multipleframes. During online fusion mode, the neural network system can performtraining and inference together. That is, the neural network system canrun one or more optimization steps to update current values ofparameters of the neural networks as if it were in the training modebefore or after computing a desired output. Online fusion allows theseneural networks to learn on the fly depth and ego-motions of unknownenvironments. This enables transfer learning across environments, forexample, by transferring models trained on data collected for robotnavigation in urban scenes to indoor navigation settings.

The details of one or more embodiments of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an architecture of an example neural network system.

FIG. 2 is a flow diagram of an example process for constructing a lossfunction for jointly training a camera motion estimation neural network,an object motion estimation neural network, and a depth predictionneural network.

FIG. 3 is a flow diagram of an example process for training the cameramotion estimation neural network, the object motion estimation neuralnetwork, and the depth prediction neural network.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification describes a neural network system implemented ascomputer programs on one or more computers in one or more locations thatincludes a camera motion estimation neural network, an object motionestimation neural network, and a depth prediction neural network.

FIG. 1 shows an example architecture of a neural network system 100. Theneural network system 100 is an example of a system implemented ascomputer programs on one or more computers in one or more locations, inwhich the systems, components, and techniques described below can beimplemented. Generally, the neural network system 100 is configured toprocess a sequence of input images to generate depth and motion outputsfor the input images.

As shown in FIG. 1, the neural network system 100 includes a cameramotion estimation neural network 104 (also referred to as “camera motionNN 104” for simplicity), an object motion estimation neural network 106(or “object motion NN 106”), and a depth prediction neural network 108(or “depth NN 108”). Each of the camera motion NN 104, the object motionNN 106, and the depth NN 108 may include one or more convolutionalneural network layers. In some implementations, the camera motion NN104, the object motion NN 106, and the depth NN 108 are fullyconvolutional neural networks.

Example architectures of the camera motion NN 104 are described in Zhou,T.; Brown, M.; Snavely, N.; and Lowe, D. 2017. “Unsupervised learning ofdepth and ego-motion from video.” Conference on Computer Vision andPattern Recognition (CVPR).

Example architectures of the depth NN 108 are described in Zhou, T.;Brown, M.; Snavely, N.; and Lowe, D. 2017, “Unsupervised learning ofdepth and ego-motion from video,” CVPR; and in Godard, C.; Aodha, O. M.;and Brostow, G. J. 2017, “Unsupervised monocular depth estimation withleft-right consistency,” CVPR.

In some implementations, the architecture of the object motion NN 106 isthe same as the camera motion NN 104 but with different parametersbecause the object motion NN 106 is configured to learn objects' motion.

An example of the object motion NN 106 is a convolutional neural networkthat has 7 convolutional neural network layers followed by a 1×1convolution followed by a mean that is applied to the output of the lxiconvolution. For example, the 1×1 convolution outputs 6 outputs and themean is applied to the 6 outputs to obtain a 6-dimensional vector.Alternatively, the object motion NN 106 can have more or fewer neuralnetwork layers, can use a fully-connected layer and can have otherchanges such as smaller dimensions.

The system 100 is configured to receive a sequence of images 102 and toprocess the sequence of images 102 using each of the neural networks104, 106 and 108 to generate a respective depth or motion output.

The sequence of input images 102 may include frames of video beingcaptured by the camera of a robotic agent. As another example, thesequence of input images 102 may include frames of a monocular videocaptured by a camera of a mobile device (e.g., by a camera of ahand-held commercial phone while a user of the phone is riding abicycle). Each of the input images include one or more potential objects(e.g., a car, truck, motorbike, bicycle, pedestrian, and animal).

In some implementations, the sequence of images 102 may includeconsecutive frames of a video. However, the sequence 102 does notnecessarily have to include all of the frames from the video. Forexample, in some implementations, the sequence 102 may include everyother frame of the video.

The depth NN 108 is configured to receive an image from the sequence 102and to process the image to generate a depth output for the image inaccordance with current values of parameters of the depth NN 108. Insome implementations, the depth NN 108 is configured to process each ofthe images in the sequence 102 to generate a respective depth output foreach image. In the example of FIG. 1, the system 100 receives a sequenceof three images (I₁, I₂, I₃). The depth NN 108 receives image I₂ asinput and processes the image I₂ to generate a depth output D₂.

A depth output generated by the depth NN 108 for a given image is adepth map that includes a predicted depth value for each pixel ofmultiple pixels in the given image, e.g., for all of the pixels or somepredetermined proper subset of the pixels. The depth value of a pixel isa representation of a perpendicular distance between (i) a plane inwhich the given image is recorded, and (ii) a scene depicted at thepixel (for example, the actual or virtual location of an object or partof an object that the pixel depicts). The plane in which the image isrecorded may be a focal plane, for example, the focal plane of a cameraof a robotic agent or the focal plane of a camera of a mobile device.

The camera motion NN 104 is generally configured to process a pair ofimages to generate a camera motion output that characterizes motion ofthe camera between the two images in accordance with current values ofparameters of the camera motion NN 104. Because there are potentialmoving objects in the input images in the sequence 102, to accuratelyestimate motion of the camera between the input images, the system 100first masks out object motions from the input images. To do this, thesystem 100 generates, for each of the input images, a respectivebackground image that includes portions of the input image that do notdepict any of the potential objects in the input image. The system 100then processes the background images using the camera motion NN 104 togenerate, for each pair of input images in the sequence 102, arespective camera motion output that characterizes motion of the camerabetween the two input images in the pair. A camera motion output is anego-motion vector that defines rotation and translation of the camerafrom its point of view while taking the first image in the pair of inputimages to its point of view while taking the second image in the pair.For example, the ego-motion vector includes three values for threetranslation components t_(x), t_(y), t_(z) and three values for threerotation components r_(x), r_(y), r_(z).

To illustrate how the system 100 generates a respective background imagefor each of the input images in the sequence 102, let (S_(i,1), S_(i,2),S_(i,3)) ∈

^(H×W) denote an instance-aligned object segmentation masks per eachpotential object i in the sequence (I₁, I₂, I₃), where H×W is the sizeof the input images, i ∈ {1, 2, . . . , N} where N is the number ofpotential objects in each of the input images in the sequence. In orderto compute camera motion, object motions are masked out of the inputimages first. More specifically, the system 100 generates a backgroundsegmentation mask by taking a complement of a union of binary objectsegmentation masks S_(i) for the potential objects in the input image asfollows:

O ₀(S)=1−∪_(i) S _(i),   (1)

where O_(j)(S)=S_(j1), j>0 returns a binary object segmentation maskonly for object j. In particular, a binary segmentation mask S_(j)includes a matrix in which each element of the matrix corresponds to arespective pixel in the input images, and each element may have a value1 or 0. If an element of the matrix has a value 1, the correspondingpixel in the input images belongs to the object j. If an element of thematrix has a value 0, the corresponding pixel in the input image doesnot belong to the object j. To generate the background segmentationmask, the system 100 takes a union of all binary object segmentationmasks and then determines an inverse of the union to obtain an areawhich does not contain any potential moving objects.

The system 100 generates a combined background segmentation mask V bytaking a pixel-wise product of the background segmentation masksgenerated for input images in the sequence:

V=O ₀(S ₁)⊙O ₀(S ₂)⊙O ₀(S ₃)   (2)

where ⊙ denotes an element-wise multiplication operation.

The system 100 generates the respective background image for each inputimage by taking a pixel-wise product of the combined backgroundsegmentation mask and the input image. The resulting sequence ofbackground images are denoted as I₁⊙V, I₂⊙V, I₃⊙V.

The system 100 provides the sequence of background images to the cameramotion NN 104 as input. The camera motion NN 104 is configured toprocess the sequence of background images to generate a camera motionoutput as follows:

E _(1→2) , E _(2→3)=ψ_(E)(I ₁ ⊙V, I ₂ ⊙V, I ₃ ⊙V)   (3)

where ψ_(E) denotes the camera motion NN 104. The camera motion outputincludes (i) a first camera motion estimate E_(1→2) that represents themotion of the camera between the first input image I₁ and the secondinput image I₂, and (ii) a second camera motion estimate E_(2→3) thatrepresents the motion of the camera between the second input image I₂and the third input image I₃. More specifically, the first camera motionestimate E_(1→2) is a first transformation matrix that transforms theposition and orientation of the camera from its point of view whiletaking the first input image to its point of view while taking thesecond input image. The second camera motion estimate E_(2→3) is asecond transformation matrix that transforms the position andorientation of the camera from its point of view while taking the secondinput image to its point of view while taking the third input image.

After processing the background images to generate the camera motionoutput, the system 100 generates, using the object motion NN 106, arespective object motion output for each of the potential objects basedon the sequence of input images and the camera motion output inaccordance with current values of parameters of the object motion NN106. The respective object motion output characterizes movements of thepotential object between its positions as appeared in the input images.

In particular, the system 100 generates a sequence of warped images,denoted as (Î_(1→2), I₂, Î_(3→2)), by applying a warping operation Ø onthe sequence of input images using the camera motion output. Morespecifically, the warping operation Ø is differentiable and can beexpressed as follows:

ϕ(I _(i) , D _(j) , E _(i→j))→Î _(i→j),   (4)

where Î_(i→j) is the reconstructed j^(th) image that is generated bywarping an input image I_(i) into I_(j) given corresponding depth outputD_(j) of input image I_(j) and a camera motion estimate E_(i→j). Foreach warped image in the sequence of warped images (Î_(1→2), I₂,Î_(3→2)), the system 100 generates a respective warped segmentationmask, denoted as (Ŝ_(1→2), S₂, Ŝ_(3→2)).

For each of the potential objects, the object motion output M^((i)) ofthe i^(th) object is computed as:

M _(1→2) ^((i)) , M _(2→3) ^((i))=ψ_(M)(Î _(1→2) ⊙O _(i)(Ŝ _(1→2)), I ₂⊙O _(i)(S ₂), Î _(3→2) ⊙O _(i)(Ŝ _(3→2))),   (5)

where ψ_(M) represents the object motion NN 106 and ⊙ denotes anelement-wise multiplication operation. M_(1→2) ^((i)) is atransformation matrix that represents motion of the potential objectbetween its first position as appeared in the first input image I₁ andits second position as appeared in the second input image I₂. M_(2→3)^((i)) is a transformation matrix that represents motion of thepotential object between its second position as appeared in the secondinput image I₂ and its third position as appeared in the third inputimage I₃.

While M_(1→2) ^((i)), M_(2→3) ^((i)) ∈ R⁶ represent object motions, theyare modeling how the camera would have moved in order to explain theobject appearance, rather than the object motion directly. As anexample, if a car is crossing an intersection from left to right, atransformation matrix would move the camera from the right to the leftsuch that, when an observer is looking at the car only, the car appearsto have moved to the right as it did.

To efficiently generate depth and motion outputs for a sequence ofimages, the neural network system 100 includes a training engine 112,which is a software-based system, subsystem, or process that isprogrammed to jointly train the camera motion NN 104, the depth NN 108and the object motion NN 106 using an unsupervised learning technique.Generally, the training engine 118 will be implemented as one or moresoftware modules or components, installed on one or more computers inone or more locations. In some cases, one or more computers will bededicated to a particular engine; in other cases, multiple engines canbe installed and running on the same computer or computers.

To jointly train the camera motion NN 104, the depth NN 108 and theobject motion NN 106, the training engine 112 determines an estimate ofa gradient of a loss function based on the sequence of warped images,the sequence of object segmentation masks, the combined backgroundsegmentation mask, the object motion outputs, the camera motion output,and the depth output generated by the system 100 and the neural networks104, 106, and 108 as described above. The training engine 112backpropagates the estimate of the gradient of the loss function tojointly adjust the current values of the parameters of camera motion NN104, the depth NM 108 and the object motion NN 106.

An example process for constructing a loss function for jointly trainingthe camera motion NN 104, the depth NN 108 and the object motion NN 106is described in detail below with reference to FIG. 2.

After the values of parameters of the neural networks 104, 106 and 108have been updated, the system 100 can process one or more new inputimages using one or more of the neural networks 104, 106 and 108 togenerate a desired output. For example, the system 100 can process a newinput image using the depth NN 108 to generate a depth output 110 forthe new input image in accordance with updated values of parameters ofthe depth output 110.

FIG. 2 is a flow diagram of an example process for constructing a lossfunction for jointly training a camera motion estimation neural network,an object motion estimation neural network, and a depth predictionneural network. For convenience, the process 200 will be described asbeing performed by a system of one or more computers located in one ormore locations. For example, a neural network system, e.g. the neuralnetwork system 100 of FIG. 1, appropriately programmed in accordancewith this specification, can perform the process 200.

The system generates a first full warped image (step 202) by performingthe following operations.

For each potential object in one or more potential objects, the systemapplies an inverse warping operation on the first warped image in thesequence of warped images, where the operation is parameterized by thedepth output D₂ and the first object motion estimate of the potentialobject to obtain Î_(1→2) ^((i)):

Î _(1→2) ^((i))=ϕ(Î _(1→2) , D ₂ , M _(1→2) ^((i)))   (6)

The system computes a pixel-wise product of Î_(1→2) ^((i)) and arespective binary object segmentation mask O_(i) (S₂) for object i togenerate a first temporary warped object image, denoted as Î_(1→2)^((i))⊙O_(i)(S₂).

The system generates a first temporary warped background image bycombining the first warped image in the sequence of warped images andthe combined background segmentation mask. The first temporary warpedbackground image is denoted as Î_(1→2)⊙V.

The system generates the first full warped image, denoted as Î_(1→2)^((F)) by combining the first temporary warped background image and thefirst temporary warped object images as follows:

$\begin{matrix}{{\hat{I}}_{1\rightarrow 2}^{(F)} = {\underset{\underset{{{Gradient}\mspace{11mu}{w.r.t.\psi_{E}}},\phi}{︸}}{{\hat{I}}_{1\rightarrow 2} \odot V} + {\sum\limits_{i = 1}^{N}\underset{\underset{{{Gradient}\mspace{11mu}{w.r.t.\psi_{M}}},\phi}{︸}}{{\hat{I}}_{1\rightarrow 2}^{(i)} \odot {O_{i}\left( S_{2} \right)}}}}} & (7)\end{matrix}$

Similarly, the system generates a second full warped image (step 204) byperforming the following operations.

For each potential object i in one or more potential objects, the systemapplies the inverse warping operation on the third warped image in thesequence of warped images, where the operation is parameterized by thedepth output D₂ and an inverse of the second object motion estimate ofthe potential object to obtain Î_(3→2) ^((i)):

Î _(3→2) ^((i))=ϕ(Î _(3→2) , D ₂ , M _(2→3) ^((i)) ⁻¹)   (8)

The system computes a pixel-wise product of Î_(3→2) ^((i)) and arespective binary object segmentation mask O_(i) (S₂) for object i togenerate a second temporary warped object image for each object i,denoted as Î_(3→2) ^((i))⊙O_(i)(S₂).

The system generates a second temporary warped background image bycombining the third warped image in the sequence of warped images andthe combined background segmentation mask. The second temporary warpedbackground image is denoted as) Î_(3→2)⊙V.

The system generates the second full warped image, denoted as Î_(2→2)^((F)) by combining the second temporary warped background image and thesecond temporary warped object images as follows:

$\begin{matrix}{{\hat{I}}_{3\rightarrow 2}^{(F)} = {\underset{\underset{{{Gradient}\mspace{11mu}{w.r.t.\psi_{E}}},\phi}{︸}}{{\hat{I}}_{3\rightarrow 2} \odot V} + {\sum\limits_{i = 1}^{N}\underset{\underset{{{Gradient}\mspace{11mu}{w.r.t.\psi_{M}}},\phi}{︸}}{{\hat{I}}_{3\rightarrow 2}^{(i)} \odot {O_{i}\left( S_{2} \right)}}}}} & (9)\end{matrix}$

After generating the first and second full warped images, the systemconstructs components of the loss function that is used for training asfollows.

The system constructs a reconstruction loss between the first and secondfull warped images and the second input image (step 206). Thereconstruction loss is computed as the minimum reconstruction lossbetween warping from either the first input image or the third inputimage into the second image (i.e., the middle image in the sequence ofthree images):

L _(rec)=min(∥Î _(1→2) ^((F)) −I ₂ ∥, ∥Î _(3→2) ^((F)) −I ₂∥)   (10)

to avoid penalization due to significant occlusion/disocclusion effects.

The system constructs a structured similarity loss that represents adissimilarity between the first and second full warped images and thesecond image (step 208). The system can construct the structuredsimilarity loss as follows:

L _(ssim)=min(1−SSIM(Î _(1→2) ^((F)) , I ₂), 1−SSIM(Î _(3→2) ^((F)) , I₂)) (11)   (11)

where SSIM(x,y) is an index that represents the similarity betweenimages patches extracted from image x and image patches extracted fromimage y. An example form of the SSIM(x,y) index is described in detailin Wang, Z.; Bovik, A. C.; Sheikh, H. R.; and Simoncelli, E. P. 2004.“Image quality assessment: from error visibility to structuralsimilarity.” Transactions on Image Processing.

The system constructs a depth smoothing loss defined by the depth outputand the second input image (step 210). The depth smoothing loss is animage-aware smoothing loss over depth predictions. It enforcessmoothness in uniform color regions while allowing depth to vary aroundimage edges:

$\begin{matrix}{L_{sm} = {{\sum\limits_{i,j}{{{\partial_{x}D^{ij}}}e^{- {{\partial_{x}\Gamma^{ij}}}}}} + {{{\partial_{y}D^{ij}}}e^{- {{\partial_{y}\Gamma^{ij}}}}}}} & (12)\end{matrix}$

where I_(i,j) denotes an image pixel at coordinates (i, j) of the givenimage I, D ^(ij) is the estimated depth corresponding with I^(ij), and∂_(x), ∂_(y) are the gradients. By considering the gradients of theimage I, the depth smoothness loss allows for sharp changes in depth atpixel coordinates where there are sharp changes in the image. Thepartial derivatives ∂_(x), ∂_(y) are for extracting the image edges inhorizontal and vertical directions. They are applied to both image andthe depth map, allowing to have a smooth depth map, i.e. with smaller inabsolute value on the edges. If the image does have an edge at aparticular location, the depth is not expected to be as smooth there,i.e. it will be penalized less for these areas.

The system constructs a loss function (step 214). The loss function is aweighted combination of (i) the reconstruction loss, (ii) the structuredsimilarity loss, and (iii) the depth smoothing loss. For example, theloss function can have the following form:

$\begin{matrix}{{L = {{\alpha_{1}{\sum\limits_{i = 0}^{3}L_{rec}^{(i)}}} + {\alpha_{2}L_{ssim}^{(i)}} + {\alpha_{3}\frac{1}{2^{i}}L_{sm}^{(i)}}}},} & (13)\end{matrix}$

where α_(i) are predetermined hyper-parameters. The total loss L can beapplied on 4 scales, i.e., the losses can be reapplied to the image andthree sub-sampled versions of the image).

In some implementations, to improve the accuracy of depth predictions,the system includes an object size loss in the above loss function toimpose object size constraints.

By imposing object size constraints, the system can address a commonissue pointed out in previous work, that objects such as cars moving infront at roughly the same speed often get projected into infinite depth.This is because the object in front shows no apparent motion, and if thenetwork estimates it as being infinitely far away, the re-projectionerror is almost reduced to zero which is preferred to the correct case.Previous work has pointed out this significant limitation but offered nosolution except for augmenting a training dataset with stereo images.However, stereo is not nearly as widely available as monocular video,which will limit the method's applicability.

It is observed that if the model has no knowledge about object scales,it could explain the same object motion by placing an object very faraway and predicting very significant motion, assuming it to be verylarge, or placing it very close and predicting little motion, assumingit to be very small. By imposing object size constraints, the systemallows the depth prediction neural network to learn objects' scales aspart of the training process, thus being able to model objects in 3D.Assuming a weak prior on the height of certain objects, e.g. a car, anapproximate depth estimation for it given its segmentation mask and thecamera intrinsics using

${D_{approx}\left( {p;h} \right)} \approx {f_{y}\frac{p}{h}}$

can be obtained, where f_(y) ∈ R is the focal length, p ∈ R is heightprior in world units, and h ∈

is a height of the respective segmentation blob in pixels.

In practice, it is not desirable to estimate such constraints by hand,and the depth prediction scale produced by the network is unknown.Therefore, the system allows the depth prediction neural network tolearn all constraints simultaneously without requiring additionalinputs.

Given the above, the system constructs the object size loss term on thescale of each object i (i=1, . . . , N) in an input image. Let t(t):

→

define a category ID for any object i, and p_(j) be a learnable heightprior for each category IDj. Let D be a depth map describing the depthestimate of each of the potential objects, and S be the correspondingobject outline mask, and D be the mean of the depth map D. The systemapplies the object size loss that represents the difference between (i)the depth prediction of each of the potential objects based on theoutput of the depth NN 108 and (ii) an approximate depth estimate at thelocation of the potential object based on a size of the potential objectin real-world as follows:

$\begin{matrix}{L_{sc} = {\sum\limits_{i = 1}^{N}{{{\frac{D \odot {O_{i}(S)}}{\overset{\_}{D}} - \frac{D_{approx}\left( {p_{t{(i)}};{h\left( {O_{i}(S)} \right)}} \right)}{\overset{\_}{D}}}}.}}} & (14)\end{matrix}$

The object size loss can effectively prevent all segmented objects todegenerate into infinite depth, and forces the network to produce notonly a reasonable depth but also matching object motion estimates.

After constructing the loss function with its loss components, thesystem generates an estimate of a gradient of the loss function andbackpropagates the estimate of the gradient to jointly adjust thecurrent values of depth parameters of the depth network and the currentvalues of motion parameters of the camera motion network (step 218). Thesystem can jointly adjust the current values of the depth and motionparameters to minimize the loss function by using mini-batch stochasticoptimization or stochastic gradient optimization method.

FIG. 3 is a flow diagram of an example process 300 for training thecamera motion estimation neural network, the object motion estimationneural network, and the depth prediction neural network. Forconvenience, the process 300 will be described as being performed by asystem of one or more computers located in one or more locations. Forexample, a neural network system, e.g., the neural network system 100 ofFIG. 1, appropriately programmed in accordance with this specification,can perform the process 300.

The system receives a sequence of input images that depict the samescene (step 302). The input images are captured by a camera at differenttime steps. Each of the input images includes one or more potentialobjects.

For each input image in the sequence of input images, the systemgenerates a respective background image that includes portions of theinput image that do not depict any of the potential objects in the inputimage (step 304).

In particular, the system generates, for each potential object in theinput image, a respective object segmentation mask for the potentialobject. The system generates a background segmentation mask for theinput image by taking a complement of a union of the object segmentationmasks for the potential objects in the input image. The system generatesthe respective background image for the input image by taking apixel-wise product of a combined background segmentation mask and theinput image. The combined background segmentation mask is a pixel-wiseproduct of the background segmentation masks generated for the inputimages in the sequence.

The system processes the background images using a camera motionestimation neural network to generate a camera motion output thatcharacterizes the motion of the camera between the input images in thesequence (step 306). The camera motion estimation neural network isconfigured to process the background images to generate the cameramotion output in accordance with current values of parameters of thecamera motion estimation neural network.

The camera motion output includes (i) a first camera motion estimatethat represents the motion of the camera between the first input imageand the second input image, and (ii) a second camera motion estimatethat represents the motion of the camera between the second input imageand the third input image. More specifically, the first camera motionestimate is a first transformation matrix that transforms the positionand orientation of the camera from its point of view while taking thefirst input image to its point of view while taking the second inputimage. The second camera motion estimate is a second transformationmatrix that transforms the position and orientation of the camera fromits point of view while taking the second input image to its point ofview while taking the third input image.

For each of the one or more potential objects, the system generates,using an object motion estimation neural network, a respective objectmotion output for the potential object based on the sequence of inputimages and the camera motion output (step 308). The respective objectmotion output characterizing movements of the potential object betweenits positions as appeared in the input images.

In particular, the respective object motion output for the potentialobject includes (i) a first object motion estimate which is a thirdtransformation matrix that represents motion of the potential objectbetween its first position as appeared in the first input image and itssecond position as appeared in the second input image, and (ii) a secondobject motion estimate which is a fourth transformation matrix thatrepresents motion of the potential object between its second position asappeared in the second input image and its third position as appeared inthe third input image. More specifically, each of the third and fourthtransformation matrices represents a motion of the potential object bydescribing a motion of the camera such that when applied and when thepotential object is considered static, the potential object appears tohave moved appropriately. As an example, if a car is crossing anintersection from left to right, a transformation matrix would move thecamera from the right to the left such that, when only looking at thecar, the car appears to have moved to the right as it did.

The system processes a particular input image of the sequence of inputimages using a depth prediction neural network and in accordance withcurrent values of parameters of the depth prediction neural network togenerate a depth output for the particular input image (step 310).

A depth output generated by the depth prediction neural network for agiven image is a depth map that includes a predicted depth value foreach pixel of multiple pixels in the given image. The depth value of apixel is a representation of a perpendicular distance between (i) aplane in which the given image is recorded, and (ii) a scene depicted atthe pixel (for example, the actual or virtual location of an object orpart of an object that the pixel depicts). The plane in which the imageis recorded may be a focal plane, for example, the focal plane of acamera of a robotic agent or the focal plane of a camera of a mobiledevice.

The system updates the current values of the parameters of the depthprediction neural network based on (i) the particular depth output forthe particular input image, (ii) the camera motion output, and (iii) theobject motion outputs for the one or more potential objects (step 312).

In particular, the system determines an estimate of a gradient of a lossfunction based on the sequence of input images, the object motionoutputs, the camera motion output, and the depth output. The system canconstruct the loss function using a method as described in detail abovewith reference to FIG. 2. The system backpropagates the estimate of thegradient of the loss function to jointly adjust the current values ofthe parameters of the camera motion estimation neural network, theobject motion estimation neural network, and the depth prediction neuralnetwork.

This specification uses the term “configured” in connection with systemsand computer program components. For a system of one or more computersto be configured to perform particular operations or actions means thatthe system has installed on it software, firmware, hardware, or acombination of them that in operation cause the system to perform theoperations or actions. For one or more computer programs to beconfigured to perform particular operations or actions means that theone or more programs include instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the operations oractions.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non-transitory storage medium for execution by, or to controlthe operation of, data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them. Alternatively or in addition, the programinstructions can be encoded on an artificially-generated propagatedsignal, e.g., a machine-generated electrical, optical, orelectromagnetic signal, that is generated to encode information fortransmission to suitable receiver apparatus for execution by a dataprocessing apparatus.

The term “data processing apparatus” refers to data processing hardwareand encompasses all kinds of apparatus, devices, and machines forprocessing data, including by way of example a programmable processor, acomputer, or multiple processors or computers. The apparatus can alsobe, or further include, special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application-specificintegrated circuit). The apparatus can optionally include, in additionto hardware, code that creates an execution environment for computerprograms, e.g., code that constitutes processor firmware, a protocolstack, a database management system, an operating system, or acombination of one or more of them.

A computer program, which may also be referred to or described as aprogram, software, a software application, an app, a module, a softwaremodule, a script, or code, can be written in any form of programminglanguage, including compiled or interpreted languages, or declarative orprocedural languages; and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A program may, but neednot, correspond to a file in a file system. A program can be stored in aportion of a file that holds other programs or data, e.g., one or morescripts stored in a markup language document, in a single file dedicatedto the program in question, or in multiple coordinated files, e.g.,files that store one or more modules, sub-programs, or portions of code.A computer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed acrossmultiple sites and interconnected by a data communication network.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby special purpose logic circuitry, e.g., an FPGA or an ASIC, or by acombination of special purpose logic circuitry and one or moreprogrammed computers.

Computers suitable for the execution of a computer program can be basedon general or special purpose microprocessors or both, or any other kindof central processing unit. Generally, a central processing unit willreceive instructions and data from a read-only memory or a random accessmemory or both. The essential elements of a computer are a centralprocessing unit for performing or executing instructions and one or morememory devices for storing instructions and data. The central processingunit and the memory can be supplemented by, or incorporated in, specialpurpose logic circuitry. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto-optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer-readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto-optical disks; andCD-ROM and DVD-ROM disks.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's device in response to requests received from the web browser.Also, a computer can interact with a user by sending text messages orother forms of message to a personal device, e.g., a smartphone that isrunning a messaging application, and receiving responsive messages fromthe user in return.

Data processing apparatus for implementing machine learning models canalso include, for example, special-purpose hardware accelerator unitsfor processing common and compute-intensive parts of machine learningtraining or production, i.e., inference, workloads.

Machine learning models can be implemented and deployed using a machinelearning framework, e.g., a TensorFlow framework, a Microsoft CognitiveToolkit framework, an Apache Singa framework, or an Apache MXNetframework.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a graphical user interface, a web browser, or anapp through which a user can interact with an implementation of thesubject matter described in this specification, or any combination ofone or more such back-end, middleware, or front-end components. Thecomponents of the system can be interconnected by any form or medium ofdigital data communication, e.g., a communication network. Examples ofcommunication networks include a local area network (LAN) and a widearea network (WAN), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other. In someembodiments, a server transmits data, e.g., an HTML page, to a userdevice, e.g., for purposes of displaying data to and receiving userinput from a user interacting with the device, which acts as a client.Data generated at the user device, e.g., a result of the userinteraction, can be received at the server from the device.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or on the scope of what may be claimed, but rather asdescriptions of features that may be specific to particular embodimentsof particular inventions. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially be claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings and recited inthe claims in a particular order, this should not be understood asrequiring that such operations be performed in the particular ordershown or in sequential order, or that all illustrated operations beperformed, to achieve desirable results. In certain circumstances,multitasking and parallel processing may be advantageous. Moreover, theseparation of various system modules and components in the embodimentsdescribed above should not be understood as requiring such separation inall embodiments, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In some cases, multitasking and parallel processing may beadvantageous.

1. A system comprising one or more computers in one or more locationsand one or more storage devices storing instructions that, when executedby one or more computers, cause the one or more computers to: receive asequence of input images that depict the same scene, the input imagesbeing captured by a camera at different time steps, each of the inputimages including one or more potential objects; generate, for each ofthe input images, a respective background image that includes portionsof the input image that do not depict any of the potential objects inthe input image; process the background images using a camera motionestimation neural network to generate a camera motion output thatcharacterizes the motion of the camera between the input images in thesequence; for each of the one or more potential objects: generate, usingan object motion estimation neural network, a respective object motionoutput for the potential object based on the sequence of input imagesand the camera motion output, the respective object motion outputcharacterizing movements of the potential object between its positionsas appeared in the input images; process a particular input image of thesequence of input images using a depth prediction neural network and inaccordance with current values of parameters of the depth predictionneural network to generate a depth output for the particular inputimage; and update the current values of the parameters of the depthprediction neural network based on (i) the particular depth output forthe particular input image, (ii) the camera motion output, and (iii) theobject motion outputs for the one or more potential objects.
 2. Thesystem of claim 1, wherein the sequence of input images are frames of avideo captured by the camera.
 3. The system of claim 1, wherein thesequence of input images comprises a first input image, a second inputimage, and a third input image.
 4. The system of claim 3, wherein thedepth output comprises an estimated depth value for each pixel of aplurality of pixels in the second image that represents a respectivedistance of a scene depicted at the pixel from a focal plane of thesecond image.
 5. The system of claim 1, wherein for each input image inthe sequence of input images, generating a respective background imagefor the input image comprises: generating a respective objectsegmentation mask for each of the potential objects in the input image,generating a background segmentation mask by taking a complement of aunion of the object segmentation masks for the potential objects in theinput image, and generating the respective background image for theinput image by taking a pixel-wise product of a combined backgroundsegmentation mask and the input image, wherein the combined backgroundsegmentation mask is a pixel-wise product of the background segmentationmasks generated for the input images in the sequence.
 6. The system ofclaim 3, wherein the instructions further comprise instructions that,when executed by the one or more computer, cause the one or morecomputers to: after processing the background images to generate thecamera motion output, generate a sequence of warped images by applying awarping operation on the sequence of input images using the cameramotion output; and wherein for each of the one or more potentialobjects, generating a respective object motion output for the potentialobject comprises: for each warped image in the sequence of warpedimages: generating a respective warped segmentation mask of thepotential object in the warped image, and generating a respective objectimage for the warped image by taking a pixel-wise product of the warpedimage and the respective warped segmentation mask; and processing, usingthe object motion estimation neural network, (i) the object image of thefirst warped image in the sequence of warped images, (ii) the secondinput image, and (iii) the object image of the third warped image in thesequence of warped images to generate the respective object motionoutput for the potential object.
 7. The system of claim 3, wherein thecamera motion output comprises (i) a first camera motion estimate thatrepresents the motion of the camera between the first input image andthe second input image and (ii) a second camera motion estimate thatrepresents the motion of the camera between the second input image andthe third input image.
 8. The system of claim 7, wherein the firstcamera motion estimate is a first transformation matrix that transformsthe position and orientation of the camera from its point of view whiletaking the first input image to its point of view while taking thesecond input image.
 9. The system of claim 7, wherein the second cameramotion estimate is a second transformation matrix that transforms theposition and orientation of the camera from its point of view whiletaking the second input image to its point of view while taking thethird input image.
 10. The system of claim 3, wherein an object motionoutput for a potential object comprises (i) a first object motionestimate which is a third transformation matrix that represents motionof the potential object between its first position as appeared in thefirst input image and its second position as appeared in the secondinput image, and (ii) a second object motion estimate which is a fourthtransformation matrix that represents motion of the potential objectbetween its second position as appeared in the second input image andits third position as appeared in the third input image.
 11. The systemof claim 1, wherein the depth prediction neural network comprises one ormore convolutional neural network layers.
 12. The system of claim 1,wherein the camera motion estimation neural network comprises one ormore convolutional neural network layers.
 13. The system of claim 1,wherein the object motion estimation neural network comprises one ormore convolutional neural network layers.
 14. The system of claim 1,wherein the camera motion estimation neural network, the object motionestimation neural network, and the depth prediction neural network havebeen jointly trained using an unsupervised learning technique.
 15. Thesystem of claim 5, wherein updating the current values of the parametersof the depth prediction neural network comprises: determine an estimateof a gradient of a loss function based on the sequence of warped images,the sequence of object segmentation masks, the combined backgroundsegmentation mask, the object motion outputs, the camera motion output,and the depth output, and backpropagate the estimate of the gradient ofthe loss function to jointly adjust the current values of the parametersof the camera motion estimation neural network, the object motionestimation neural network, and the depth prediction neural network. 16.The system of claim 15, wherein determining the estimate of the gradientof the loss function comprises: generating a first full warped image byperforming the following operations: for each potential object in one ormore potential objects, applying an inverse warping operation on thefirst warped image in the sequence of warped images, wherein theoperation is parameterized by the depth output for the particular inputimage and the first object motion estimate of the potential object, andcombining the result with the respective object segmentation mask togenerate a first temporary warped object image, generating a firsttemporary warped background image by combining the first warped image inthe sequence of warped images and the combined background segmentationmask, generating the first full warped image by combining the firsttemporary warped background image and the first temporary warped objectimages; generating a second full warped image by performing thefollowing operations: for each potential object in one or more potentialobjects, applying the inverse warping operation on the third warpedimage in the sequence of warped images, wherein the operation isparameterized by the depth output for the particular input image and thesecond object motion estimate of the potential object, and combining theresult with the respective object segmentation mask to generate a secondtemporary warped object image, generating a second temporary warpedbackground image by combining the third warped image in the sequence ofwarped images and the combined background segmentation mask, generatingthe second full warped image by combining the second temporary warpedbackground image and the second temporary warped object images; andwherein the loss function comprises (i) a first component thatrepresents a reconstruction loss between the first and second fullwarped images and the second input image, (ii) a second component thatrepresents a dissimilarity between the first and second full warpedimages and the second image, and (iii) a third component that representsa depth smoothing loss defined by the depth output and the second inputimage.
 17. The system of claim 16, wherein the loss function furthercomprises an object size loss component that represents the differencebetween (i) the depth prediction of each of the potential objects basedon the output of the depth prediction neural network, and (ii) anapproximate depth estimate at the location of the potential object basedon a size of the potential object in real-world.
 18. A methodcomprising: receiving a sequence of input images that depict the samescene, the input images being captured by a camera at different timesteps, each of the input images including one or more potential objects;generating, for each of the input images, a respective background imagethat includes portions of the input image that do not depict any of thepotential objects in the input image; processing the background imagesusing a camera motion estimation neural network to generate a cameramotion output that characterizes the motion of the camera between theinput images in the sequence; for each of the one or more potentialobjects: generating, using an object motion estimation neural network, arespective object motion output for the potential object based on thesequence of input images and the camera motion output, the respectiveobject motion output characterizing movements of the potential objectbetween its positions as appeared in the input images; processing aparticular input image of the sequence of input images using a depthprediction neural network and in accordance with current values ofparameters of the depth prediction neural network to generate a depthoutput for the particular input image; and updating the current valuesof the parameters of the depth prediction neural network based on (i)the particular depth output for the particular input image, (ii) thecamera motion output, and (iii) the object motion outputs for the one ormore potential objects.
 19. The method of claim 18, further comprising:receiving an image as input; processing the image according to currentvalues of parameters of the depth prediction neural network to generatean estimate of depth of the input image.
 20. One or more computerstorage media encoded with instructions that, when executed by one ormore computers, cause the one or more computers to perform operationscomprising: receiving a sequence of input images that depict the samescene, the input images being captured by a camera at different timesteps, each of the input images including one or more potential objects;generating, for each of the input images, a respective background imagethat includes portions of the input image that do not depict any of thepotential objects in the input image; processing the background imagesusing a camera motion estimation neural network to generate a cameramotion output that characterizes the motion of the camera between theinput images in the sequence; for each of the one or more potentialobjects: generating, using an object motion estimation neural network, arespective object motion output for the potential object based on thesequence of input images and the camera motion output, the respectiveobject motion output characterizing movements of the potential objectbetween its positions as appeared in the input images; processing aparticular input image of the sequence of input images using a depthprediction neural network and in accordance with current values ofparameters of the depth prediction neural network to generate a depthoutput for the particular input image; and updating the current valuesof the parameters of the depth prediction neural network based on (i)the particular depth output for the particular input image, (ii) thecamera motion output, and (iii) the object motion outputs for the one ormore potential objects.